I had a vx2100 for about a year before i sold it (for a car). I miss that camera like no other, and while I can't lay claim to having used a vx2k for more than 10 minutes, the footage is not going to be different. Perhaps some different adjustments to achieve the same look, but they'll put out the same picture that the other one does if used properly. It takes much getting used to if it's your first prosumer camera, but if you're worried about which will give you better picture, they're equal.
Now that that is aside (which is my opinion, btw), having a record button on the handle was extremely convenient. The vx2100 is slightly heavier and a little bit bulkier. It also has better capabilities in low light.
And I haven't read it in any posts before mine, but a lot of people left out a huge reason for sticking to the older vx1k - using the mk1